Partial regularity for the Navier-Stokes equations with a force in a Morrey space |
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Authors: | Igor Kukavica |
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Affiliation: | Department of Mathematics, University of Southern California, Los Angeles, CA 90089, United States |
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Abstract: | In the paper, we address the partial regularity of solutions of the Navier-Stokes system. Earlier, we have proved that the one-dimensional parabolic Hausdorff measure of the singular set is zero under the assumption that the force f belongs locally to L5/3. Here we prove the same statement under a more general assumption that the Morrey norm in of the force is sufficiently small. We do so by establishing a fractional integration theorem using the Morrey spaces and by a suitable iteration using a localized version of the Morrey norm. |
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Keywords: | Navier-Stokes equation Partial regularity Morrey space |
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